We argue that the light-enhanced entanglement likely reflects the proximity to a quantum phase transition. Although our trRIXS simulation is restricted to a small cluster and cannot rigorously determine phase boundaries, we compare the QFI dynamics under the same excitation conditions in the EHM and in a doped Hubbard model (without the attractive \(V\) ). While the two Hamiltonians only differ by a \(V\sim -t_h\)  term, much smaller than the dominant on-site interaction \(U=8t_h\) , previous studies have shown the presence of a triplet superconducting phase for moderate attractive near-neighbor interactions [1]}, [2]}, [3]}, [4]}, [5]}.
This phase transition boundary has been explored through exact numerical methods in the thermodynamic limit, suggesting that, for \(U=8t_h\) , triplet superconductivity develops for \(-1.7t_h\lesssim V\lesssim -1.1t_h\)  [6]}. Therefore, the EHM with \(V= -t_h\)  is expected to display a stronger light-induced entanglement due to the proximity to this phase boundary. As shown in Figs. REF (c) and (d), the QFI of the driven Hubbard model (without \(V\) ) is much smaller than that of the EHM at same pump conditions, consistent with the absence of such quantum phase transition in the former model.
